"""simple docstring"""


from __future__ import annotations

a				='#'






class   __UpperCAmelCase		:

				def __init__( self ):
										lowerCamelCase__   ={}

				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =self._trie
										for char in text:
																if char not in trie:
																						lowerCamelCase__   ={}
																lowerCamelCase__   =trie[char]
										lowerCamelCase__   =True

				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =self._trie
										for char in prefix:
																if char in trie:
																						lowerCamelCase__   =trie[char]
																else:
																						return []
										return self._elements(_lowerCamelCase )






				def 						_a      ( self      ,					_lowerCamelCase ):
										lowerCamelCase__   =[]
										for c, v in d.items():
																lowerCamelCase__   =[" "] if c == END else [(c + s) for s in self._elements(_lowerCamelCase )]
																result.extend(_lowerCamelCase )
										return tuple(_lowerCamelCase )





a				=Trie()
a				=('depart', 'detergent', 'daring', 'dog', 'deer', 'deal')
for word in words:
	trie.insert_word(word)





def      lowerCamelCase_					(   __lowerCAmelCase							)				->   tuple:




						'''simple docstring'''



						lowerCamelCase__   =trie.find_word(__lowerCAmelCase							)
						return tuple(string + word for word in suffixes							)





def      lowerCamelCase_					(   )				->   None:




						'''simple docstring'''



						print(autocomplete_using_trie("de"							)							)


if __name__ == "__main__":
	import doctest

	doctest.testmod()
	main()



"""simple docstring"""


def      lowerCamelCase_					(   __lowerCAmelCase							)				->   "list[int]":




						'''simple docstring'''



						if upper_limit < 0:
												raise ValueError("Limit for the Catalan sequence must be ≥ 0"							)

						lowerCamelCase__   =[0] * (upper_limit + 1)

						# Base case: C(0) = C(1) = 1
						lowerCamelCase__   =1
						if upper_limit > 0:
												lowerCamelCase__   =1

						# Recurrence relation: C(i) = sum(C(j).C(i-j-1)), from j = 0 to i
						for i in range(2  ,       upper_limit + 1							):
												for j in range(__lowerCAmelCase							):
																		catalan_list[i] += catalan_list[j] * catalan_list[i - j - 1]

						return catalan_list


if __name__ == "__main__":
	print('\n********* Catalan Numbers Using Dynamic Programming ************\n')
	print('\n*** Enter -1 at any time to quit ***')
	print('\nEnter the upper limit (≥ 0) for the Catalan number sequence: ', end='')
	try:
		while True:
			a				=int(input().strip())
			if N < 0:
				print('\n********* Goodbye!! ************')
				break
			else:
				print(F'''The Catalan numbers from 0 through {N} are:''')
				print(catalan_numbers(N))
				print('Try another upper limit for the sequence: ', end='')
	except (NameError, ValueError):
		print('\n********* Invalid input, goodbye! ************\n')

	import doctest

	doctest.testmod()


